Recall that we denote by \(\text{Max}(S)\) 
the space of conjugacy classes of representations \(\rho =(\rho _1,\rho _2)\)  of the fundamental group of a closed connected oriented surface \(S\)  of negative Euler characteristic into the Lie group \(\mathrm {PSL}(2,\mathbb {R})\times \mathrm {PSL}(2,\mathbb {R})\)  such that \(e(\rho _1)+e(\rho _2)=4g-4\) . Here, \(e\)  denotes the Euler number of the representation. It follows from [1]} that \(\rho _1\)  and \(\rho _2\)  are both Fuchsian representations. Therefore, as \(\text{Max}(S)\)  may be thought of as the product of two copies of Teichmüller space, it is homeomorphic to an open cell of dimension \(12g-12\) .
